Eric, Dylan and Ivan had a total of 139 buttons. The ratio of the number of buttons that Dylan had to the number of buttons that Ivan had was 4 : 7. After Eric and Dylan each gave away half of their buttons, the 3 children had 108 buttons left. How many buttons did Dylan and Ivan have in the end?
| |
Eric |
Dylan |
Ivan |
Total |
| Before |
2 p |
4 u |
7 u |
139 |
| Change |
- 1 p |
- 2 u |
|
- 31 |
| After |
1 p |
2 u |
7 u |
108 |
Total number of buttons that Eric and Dylan gave away
= 139 - 108
= 31
1 p + 2 u = 31 --- (1)
1 p + 2 u + 7 u = 108
1 p + 9 u = 108 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 2 u) = 108 - 31
9 u - 2 u = 77
7 u = 77
1 u = 77 ÷ 7 = 11
Total number of buttons that Dylan and Ivan had in the end
= 2 u + 7 u
= 9 u
= 9 x 11
= 99
Answer(s): 99
